A viscosity solution approach to regularity properties of the optimal value function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Ochoa, Pablo^1,2  Vera de Serio, Virginia N.³ 

[1] Consejo Nacl Invest Cient & Tecn, Mendoza, Argentina

[2] Univ Nacl Cuyo, Fac Ingn, Mendoza, Argentina

[3] Univ Nacl Cuyo, Fac Ciencias Econ, Mendoza, Argentina

关键词: Viscosity solutions;    Parametric optimization;    Optimal value function;    Lipschitz continuity;    Generalized derivative;   

DOI  :  10.1016/j.jmaa.2021.125470

来源: Elsevier

【 摘 要 】

We analyze the optimal value function v associated with a general parametric optimization problem via the theory of viscosity solutions. The novelty is that we obtain regularity properties of v by showing that it is a viscosity solution to a set of first-order equations. As a consequence, in Banach spaces, we provide sufficient conditions for local and global Lipschitz properties of v. We also derive, in finite dimensions, conditions for optimality through a comparison principle. Finally, we study the relationship between viscosity and Clarke generalized solutions to get further differentiability properties of v in Euclidean spaces. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free